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Ratio Solver & Proportion Calculator

Ratio Solver

Solve for the missing value or check if a ratio is true.

Decimals
2
A
B
C
D
: = :
Leave one field empty to solve for it. Fill all four to check validity.
Enter values above to see the result here...
Calculates in real-time
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How the Ratio Solver Works

This tool uses the cross-product property of proportions to solve ratio equations. A proportion takes the form A : B = C : D.

The fundamental rule is that the product of the extremes (A and D) must equal the product of the means (B and C):

A × D = B × C

Solving for a Missing Value

If you leave one field empty, the calculator isolates that variable:

  • Missing A: A = (B × C) / D
  • Missing B: B = (A × D) / C
  • Missing C: C = (A × D) / B
  • Missing D: D = (B × C) / A

Checking True/False

If you enter values for all four fields, the Ratio Solver compares the cross-products. If (A × D) equals (B × C), the ratio is TRUE. If not, it returns FALSE.

Frequently Asked Questions

How do I convert a Ratio to a Fraction?
A ratio A:B can be written directly as the fraction A/B. For example, the ratio 3:4 is the fraction 3/4.
What is the "Golden Ratio"?
The Golden Ratio is a special number approximately equal to 1.618. It appears frequently in geometry, art, architecture, and nature. In a ratio form, it is roughly 1 : 1.618.
How do I simplify a ratio?
To simplify a ratio, find the Greatest Common Divisor (GCD) of the numbers and divide both by it. For example, 10:15. The GCD is 5. Divide both by 5 to get 2:3.
How do I solve a ratio?
To solve a ratio like A : B = C : D, you use the cross-product method. Multiply the diagonals (A × D) and (B × C). If one value is missing, divide the known product by the remaining number.
How do I calculate the missing value x?
If your equation is 1 : 2 = 3 : x, multiply the means (2 × 3 = 6) and divide by the extreme (1). So x = 6.
What are equivalent ratios?
Equivalent ratios are ratios that express the same relationship between numbers. For example, 1:2 and 2:4 are equivalent because they both simplify to 0.5.
How do I check if a ratio is true or false?
Enter all four values into the calculator. If A × D equals B × C, the ratio is TRUE. If they are not equal, it is FALSE.